Strongly Gorenstein projective, injective, and flat modules

  title={Strongly Gorenstein projective, injective, and flat modules},
  author={Najib Mahdou and Mohammed Tamekkante},
  journal={Journal of Pure and Applied Algebra},
Notes on Gorenstein Flat Modules
In this paper, we explore conditions under which Gorenstein flat modules are Gorenstein projective. We prove that all countably presented strongly Gorenstein flat modules are Gorenstein projective
When Every Gorenstein Projective (Resp. Flat) Module is Strongly Gorenstein Projective (Resp. Flat)
In [5], the authors discuss the rings over which all modules are strongly Gorenstein projective. In this paper, we are interesting to an extension of this idea. Thus, we discuss the rings over which
n -Strongly Gorenstein Projective and Injective Complexes
In this paper, we introduce and study the notions of n-strongly Gorenstein projective and injective complexes, which are generalizations of n-strongly Gorenstein projective and injective modules,
A Characterization of Gorenstein Projective Modules
In this article, we give a new characterization of Gorenstein projective modules. As applications of our result, we prove that a strongly Gorenstein projective module of countable type is Gorenstein
Gorenstein FC-projective modules
  • Yu WangDexu Zhou
  • Mathematics, Physics
    Journal of Algebra and Its Applications
  • 2019
In this paper, we investigate Gorenstein FC-projective modules and Gorenstein FC-projective dimensions, and characterize rings over which every module is Gorenstein FC-projective and rings over which
Abstract In this paper, strongly Gorenstein flat modules are introduced and investigated. An R-module M is called strongly Gorenstein flat if there is an exact sequence ⋯→P1→P0→P0→P1→⋯ of projective
On Strongly Gorenstein FP-Injective Modules
This article continues to investigate a particular case of Gorenstein FP-injective modules, called strongly Gorenstein FP-injective modules. Some examples are given to show that strongly Gorenstein
Strongly Gorenstein flat and Gorenstein FP-injective modules
In this paper, we first study the properties of strongly Gorenstein flat (resp. Gorenstein FP-injective) modules which are special Gorenstein projective (resp. Gorenstein injective) modules, and use
(n, m)-Strongly Gorenstein Projective, Injective and Flat Modules
Some properties of -Strongly Gorenstein projective ,injective and flat modules are studied and some connections between -Strongly Gorenstein projective , injective and flat modules are discussed . At


On Gorenstein Flat Modules
In order to research the structure and properties of modulcs overings and algebras,In this paper,by using homological methods we investigated the ralation between Gorenstein injective modules and
Gorenstein homological dimensions
Relative homological coalgebras
We study classes of relative injective and projective comodules and extend well-known results about projective comodules given in [7]. The existence of covers and envelopes by these classes of
Foxby duality and Gorenstein injective and projective modules
In 1966, Auslander introduced the notion of the G-dimension of a finitely generated module over a Cohen-Macaulay noetherian ring and found the basic properties of these dimensions. His results were
On finitely generated flat modules
Introduction. The aim of this paper is to study conditions which reflect the projectivity of a given finitely generated flat module over a commutative ring. The use of the invariant factors of a
Finitely Generated Flat Modules and a Characterization of Semiperfect Rings
Abstract For a ring S, let K 0(FGFl(S)) and K 0(FGPr(S)) denote the Grothendieck groups of the category of all finitely generated flat S-modules and the category of all finitely generated projective
Absolute, Relative, and Tate Cohomology of Modules of Finite Gorenstein Dimension
We study finitely generated modules M over a ring R, noetherian on both sides. If M has finite Gorenstein dimension G‐dimRM in the sense of Auslander and Bridger, then it determines two other
An introduction to homological algebra
Preface 1. Generalities concerning modules 2. Tensor products and groups of homomorphisms 3. Categories and functors 4. Homology functors 5. Projective and injective modules 6. Derived functors 7.
Flat covers of modules
Envelopes and covers.- Fundamental theorems.- Flat covers and cotorsion envelopes.- Flat covers over commutative rings.- Applications in commutative rings.